As you stated, the effects of overnight/morning convection are variable and not always as straightforward as they might seem.
The main things I look for are:
1.) Does it clear in time for several hours of sun/heating before the later round?
2.) It is an organized MCS that leaves a large cold pool? In this case, even clearing behind it may not be enough for airmass recovery in the area where it tracked, but wherever the outflow boundary sets up could become the new target (this occurred in northern Illinois on June 22, 2015 after a large midmorning MCS swept through the original tornado threat area of southern Wisconsin).
We had thunderstorms around 8 AM on the morning of the state-record tornado outbreak of August 18, 2005 which included the long-track F3 Stoughton tornado. However they were out of the area and skies were partly cloudy by early afternoon.
I'd seen morning convection screw up enough setups that I made a painful mistake on the Pilger day in 2014. I was heading west on US-20 in Iowa with a target of Sioux City by 3 PM. However, at a late morning data stop (this was before I had a smartphone and thus data on the fly) I noticed a region of ongoing rain over the Missouri River on the IA/NE border. At this I made a snap decision to retarget south to Omaha, which was south of the area being rained on and in clear skies.
The trek south on I-35 to Des Moines and west on I-80 put me just far enough away from the Pilger supercell to reach it blasting north on US-77 just as it produced the last-gasp bird fart tornado near Hubbard (seen from just north of Winnebago), then collapsed as it indeed hit the area stabilized by the rain I had been worried about earlier. The area where the storm had gone nuts just a little bit to the west had cleared out earlier, and destabilized to become an extremely volatile environment.
The morning QLCS in MS/AL on 4/27/11 was an unusual beast. It was clearly a very organized system, and produced enough tornadoes (including several long-track EF2-3) to more than verify a high risk even without the violent outbreak later in the day. However it was largely out of the area by or shortly after dawn, allowing for strong heating in its wake. It left an outflow boundary that served to enhance many of the most violent tornadoes that day, including Cullman and Hackleburg. However the conditions that day were so ideal that many other storms in the open warm sector were able to become cyclic, violent tornado machines.
Areas further to the north in middle/northern TN, KY, IN, OH were in fact stabilized by repeated rounds of convection through the midday, which may have been the only thing that prevented violent tornado activity there, thus being the only thing in my mind that prevents that day from being unquestionably equal to or worse than the 1974 Super Outbreak in every metric.
